Is there a specific reason why The Last Days of a Famous Mime is divided into 16 parts: is it structured almost like a drama?
The story The Last Days of a Famous Mime is divided into sixteen different parts. Given that the text offers an examination of both the art of mime and the artist practicing the art of mime, the story exists in a disjointed fashion which mirrors the art of miming itself. Mimes typically tell short disjointed stories through their art and the text illuminates this fact.
Outside of that, given that mime do not speak, the text is limited in "dialogue." A mime's stories are short and concise. They are trying to get their viewers to examine a very simplistic idea or action which can only be described through motion and non-verbal communication. Therefore, the sixteen different parts mimic the language of the mime: fragmented, direct, and minimal.
To explain further, picture a mime in action. Their "dialogue" with their audience is very controlled and they only "say" what is absolutely necessary to depict what needs to be depicted. The text, therefore, follows this practice. A long and elaborate description would nullify their art given their art is, in part, simplistic in nature (for the viewer--not the artist).